$\dfrac{d}{dx}\left(\sqrt[4]{x}\right)=$
The strategy We can first rewrite the radical as a rational power of $x$. Then, the derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a fraction.) Rewriting the radical as a rational power $\sqrt[4]{x}=x^{^{\frac{1}{4}}}$ Differentiating using the power rule $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{^{\frac{1}{4}}}\right) \\\\ &=\dfrac{1}{4}x^{^{\frac{1}{4}-1}} \gray{\text{The power rule}} \\\\ &=\dfrac{1}{4}x^{^{-\frac{3}{4}}} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(\sqrt[4]{x}\right)=\dfrac{1}{4}x^{^{-\frac{3}{4}}}$. This can also be written as $\dfrac{1}{4\sqrt[4]{x^3}}$ (all equivalent forms are accepted).